Separate the 13 spades from a standard deck of cards. Three of them are picture

Question

Separate the 13 spades from a standard deck of cards. Three of them are picture cards: the Jack, Queen, and King. Now draw two cards at random from these 13 spades. Find the probability (rounded to the nearest .01%) that (a) both of the cards drawn are picture cards, if they are drawn i. without replacement. ii. with replacement. (b) at least one of the two cards drawn is a picture card, if they are drawn i. without replacement. ii. with replacement. An 11-digit number is randomly chosen by drawing 11 times from a box that has one ticket for each of the numbers 0 to 9 and writing down the numbers on the tickets in the order in which they are drawn. Find the chance that exactly 2 of the digits in the number chosen are sevens.

Explanation / Answer

4)

a-1)

3/13*2/12=0.0384

a-2)

3/13*2/13=0.0355

b-1)

3/13*2/12+3/13*10/12=0.2307

b-2)

3/13*2/13+3/13*10/13=0.2130

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